Find the projection of the vector ( i - j ) on the vector ( i + j ).

Let \(\vec{a}\)= (\(\hat{i}\)- \(\hat{j}\))  and \(\vec{b}\) = (\(\hat{i}\)+ \(\hat{j}\))

Now, projection of \(\vec{a}\) on \(\vec{b}\) is given by,

(\(\vec{a}\).\(\vec{b}\))/|\(\vec{b}\)| = {1.1 + (-1).1}/√(1+1) = 0

Hence, the projection of vector (\(\hat{i}\)- \(\hat{j}\)) on the vector  (\(\hat{i}\)+ \(\hat{j}\)) is 0.